Sign In or Sign Up

This means that if you are signing in for  one session,  the correct word is  log in. So, for the user, it could be  sign in  but for the system, it's  log in.

It is for this reason, content management software/portal like  WordPress  uses  log in  because it  maintains the log  each time you  sign in  and  sign out  which will complete the cycle of  one session. It is for this reason  again,  the computer asks to  log in  and not  sign in. After all, you enter and come out completing  one cycle  i.e. session.

What I prefer is asking the user to  log in  if you are strictly maintaining the record (--say WordPress or Bank portal) and in other case where maintaining  log  is not so important (say a subscription for the newsletter, jokes, pranks or the like)  sign in.

While using these words, it's important that you stick to one style. If you ask the user to  log in, give them an option of  log out  and not  sign out  and vice versa.